At what rate per cent per annum simple interest will a sum double itself in 10 years?

Options

A. `8%`
B. `10%`
C. `12%`
D. `12.1/2%`

Answer

To find the rate per cent per annum at which a sum will double itself in 10 years using simple interest, we can follow these steps:

### Step 1: Understand the Problem
We need to determine the rate of interest (r) that will allow a principal amount (P) to double in 10 years.

### Step 2: Define the Principal and Amount
Let the principal amount be \( P = x \). Since the sum doubles, the amount after 10 years will be:
\[ A = 2x \]

### Step 3: Use the Formula for Amount
The formula for the amount (A) in terms of principal (P) and simple interest (SI) is:
\[ A = P + SI \]
Substituting the values we have:
\[ 2x = x + SI \]

### Step 4: Solve for Simple Interest
Rearranging the equation to find simple interest (SI):
\[ SI = 2x - x = x \]

### Step 5: Use the Simple Interest Formula
The formula for simple interest is:
\[ SI = \frac{P \times r \times t}{100} \]
Substituting the values we have:
\[ x = \frac{x \times r \times 10}{100} \]

### Step 6: Simplify the Equation
We can simplify this equation. First, we can cancel \( x \) from both sides (assuming \( x \neq 0 \)):
\[ 1 = \frac{r \times 10}{100} \]

### Step 7: Solve for Rate (r)
Now, multiply both sides by 100 to eliminate the fraction:
\[ 100 = r \times 10 \]
Dividing both sides by 10 gives:
\[ r = 10 \]

### Conclusion
The rate of interest per annum is:
\[ \text{Rate} = 10\% \]

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